Find Largest Square Tile Side Length
To use the smallest number of identical square tiles, the side length of each tile must be as large as possible.
The side length of the square tile must perfectly divide both the length (24 units) and the width (18 units) of the floor.
Therefore, the side length must be the Greatest Common Divisor (GCD) of 18 and 24.
- Factors of 18: 1, 2, 3, 4, 6, 9, 18
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- The GCD of 18 and 24 is 6.
So, the largest possible identical square tile has a side length of 6 units.
Calculate Number of Tiles
The number of tiles needed is determined by how many tiles fit along each dimension of the floor.
- Number of tiles along the 18-unit side: $ \frac{18}{6} = 3 $ tiles
- Number of tiles along the 24-unit side: $ \frac{24}{6} = 4 $ tiles
Total number of tiles = (Tiles along width) $ \times $ (Tiles along length)
Total number of tiles = $ 3 \times 4 = 12 $ tiles.
Alternatively, using area:
- Floor Area = $ 18 \times 24 = 432 $ square units.
- Tile Area = $ 6 \times 6 = 36 $ square units.
- Number of Tiles = $ \frac{\text{Floor Area}}{\text{Tile Area}} = \frac{432}{36} = 12 $.
The smallest number of identical square tiles required is 12.
Important Questions from Geometry (Notes)
- Which of the following is not true for a parallelogram?
- A 6 cm long chord of a circle is at a distance of 4 cm from the centre of the circle. Find the distance of 8 cm long chord of the same circle from the centre.
- The length of major axis and coordinate of vertices for the ellipse $3x^2 + 2y^2 = 6$ respectively are:
- If the line through (3, y) and (2, 7) is parallel to the line through (-1, 4) and (0,6), then the value of y is:
- The points (K, 2 – 2K), (-K +1,2K) and (-4-K, 6-2K) are collinear if:
(A) K = $\frac{1}{2}$
(B) K = $-\frac{1}{2}$
(C) K = $\frac{3}{2}$
(D) K = -1
(E) K = 1
Choose the correct answer from the options given below:
